(5-c)(3c-5)=7c

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Solution for (5-c)(3c-5)=7c equation:


Simplifying
(5 + -1c)(3c + -5) = 7c

Reorder the terms:
(5 + -1c)(-5 + 3c) = 7c

Multiply (5 + -1c) * (-5 + 3c)
(5(-5 + 3c) + -1c * (-5 + 3c)) = 7c
((-5 * 5 + 3c * 5) + -1c * (-5 + 3c)) = 7c
((-25 + 15c) + -1c * (-5 + 3c)) = 7c
(-25 + 15c + (-5 * -1c + 3c * -1c)) = 7c
(-25 + 15c + (5c + -3c2)) = 7c

Combine like terms: 15c + 5c = 20c
(-25 + 20c + -3c2) = 7c

Solving
-25 + 20c + -3c2 = 7c

Solving for variable 'c'.

Reorder the terms:
-25 + 20c + -7c + -3c2 = 7c + -7c

Combine like terms: 20c + -7c = 13c
-25 + 13c + -3c2 = 7c + -7c

Combine like terms: 7c + -7c = 0
-25 + 13c + -3c2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
8.333333333 + -4.333333333c + c2 = 0

Move the constant term to the right:

Add '-8.333333333' to each side of the equation.
8.333333333 + -4.333333333c + -8.333333333 + c2 = 0 + -8.333333333

Reorder the terms:
8.333333333 + -8.333333333 + -4.333333333c + c2 = 0 + -8.333333333

Combine like terms: 8.333333333 + -8.333333333 = 0.000000000
0.000000000 + -4.333333333c + c2 = 0 + -8.333333333
-4.333333333c + c2 = 0 + -8.333333333

Combine like terms: 0 + -8.333333333 = -8.333333333
-4.333333333c + c2 = -8.333333333

The c term is -4.333333333c.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333c + 4.694444446 + c2 = -8.333333333 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333c + c2 = -8.333333333 + 4.694444446

Combine like terms: -8.333333333 + 4.694444446 = -3.638888887
4.694444446 + -4.333333333c + c2 = -3.638888887

Factor a perfect square on the left side:
(c + -2.166666667)(c + -2.166666667) = -3.638888887

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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